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Generalized Functions, Volume 4 - Applications of Harmonic Analysis (Hardcover)
Loot Price: R1,822
Discovery Miles 18 220
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Generalized Functions, Volume 4 - Applications of Harmonic Analysis (Hardcover)
Series: AMS Chelsea Publishing
Expected to ship within 12 - 17 working days
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Total price: R1,842
Discovery Miles: 18 420
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The first systematic theory of generalized functions (also known as
distributions) was created in the early 1950s, although some
aspects were developed much earlier, most notably in the definition
of the Green's function in mathematics and in the work of Paul
Dirac on quantum electrodynamics in physics. The six-volume
collection, Generalized Functions, written by I. M. Gelfand and
co-authors and published in Russian between 1958 and 1966, gives an
introduction to generalized functions and presents various
applications to analysis, PDE, stochastic processes, and
representation theory. The main goal of Volume 4 is to develop the
functional analysis setup for the universe of generalized
functions. The main notion introduced in this volume is the notion
of rigged Hilbert space (also known as the equipped Hilbert space,
or Gelfand triple). Such space is, in fact, a triple of topological
vector spaces $E \subset H \subset E'$, where $H$ is a Hilbert
space, $E'$ is dual to $E$, and inclusions $E\subset H$ and
$H\subset E'$ are nuclear operators. The book is devoted to various
applications of this notion, such as the theory of positive
definite generalized functions, the theory of generalized
stochastic processes, and the study of measures on linear
topological spaces.
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